The Efficient Scheduling Algorithm For Maximizing Computer Science Essay

Published Date: 02 Nov 2017

J. ROSELIN, S. LATHA, S. UMA MAHESWARI

Department of Computer Science and Engineering

Anna University

Tirunelveli

INDIA

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Abstract: - Coverage is associated with energy-efficiency and network lifetime in wireless sensor network. Generally, there is tradeoff between sensing coverage and network lifetime. Both coverage and network lifetime cannot be satisfied at the same time since both has direct impact on batteries energy consumption. This system maximizes the coverage while minimizing the coverage redundancy with network lifetime as constraint. The objective is to maximize the coverage in wireless sensor network by scheduling sensors activity after random deployment. This system proposes a distributed parallel optimization protocol (POP). This protocol optimizes the on-period of each sensor schedules which converges to local optimality without conflict to one another. The simulation results show that the distributed algorithm substantially outperforms other schemes in terms of energy consumption, coverage redundancy and convergence time.

Key-words— Wireless sensor network, coverage, network lifetime, sensor scheduling, distributed algorithm, independent set.

Introduction

Wireless sensor networks have vast development in the area of research and commercial applications. These networks are typically used to monitor a field of interest to detect movement, temperature changes, precipitation, etc. A wireless sensor network composes of a large scale of sensor devices (called sensor nodes). Each sensor node is equipped with sensor unit, a wireless communication unit, a battery power unit and a programmable embedded processor. The sensor nodes are capable of sensing, data processing, and communicating with each other via radio transceivers.

Coverage of wireless sensors is the parameter of our concern in this paper. Coverage refers to the sensing region of a node i.e. a sensor can detect a parameter only if it lies within the coverage of the concerned node.

In wireless sensor networks, there is a trade-off between network lifetime and sensor coverage. To achieve a better coverage, more sensors are put in to active at the same time, then more energy would be consumed and the network life time is reduced. On the other hand, if more sensors are put into sleep to extend the network lifetime, the coverage will be adversely affected. The trade-off between network lifetime and sensor coverage cannot be simply solved at the deployment stage, because it is hard to predict the network lifetime requirement, which depends on the application and may change as the mission changes.

Various scheduling schemes are addressed for the coverage problem to maximize the network lifetime while maintaining some predefined coverage degree [1- 6]. However, if the same coverage degree is maintained all the time, the lifetime requirements may not be satisfied as network condition and mission changes. Different from existing works, we study how to schedule sensor’s active time to maximize coverage under the constraint of network lifetime.

We have to consider coverage in both spatial and temporal domain. The spatial-temporal coverage of each small area is defined as the product of the area size and the length of the period during which the area is covered [22]. Then, our objective becomes how to schedule the sensor’s on-period to maximize the global spatial-temporal coverage.

Scheduling sensor nodes is an important method to conserve energy resources. In this system the distributed algorithm that efficiently organize or schedule the sensor activity after random deployment are very efficient and have a direct impact with the spatial-temporal coverage maximization.

This paper addresses a scheduling scheme for each node to optimize their schedule to maximize the coverage at the point of an interest area. This scheme is based on an assumption of unstructured WSN which contains a dense collection of sensor nodes, which are randomly placed into the field (i.e., deployed in an ad-hoc manner) of an interest area [23]. By scheduling the devices’ activities, the overlapping "on" periods of sensor can be minimized to achieve prolong lifetime. This efficient scheduling scheme use only limited amount of energy.

The aim of this system is to schedule sensors to maximize their spatial-temporal coverage during a specified network lifetime, and to minimize the spatial-temporal coverage redundancy.

In this work, we present a novel scheduling scheme, which is used to configure node work status and schedule the sensor on-period time in large sensor networks. Our design was driven by the following requirements. First, since it is inconvenient or impossible to manually configure sensors after they have been deployed in hostile or remote working environment, self configuration is mandated. Second, the design has to be fully distributed and localized, because a centralized algorithm needs significant overhead for global synchronization and is not scalable to large-populated networks [12]. Third, proposing a distributed parallel optimization protocol (POP) which provides the effective scheduling in terms of coverage and lifetime.

The rest of the paper is organized as follows: Section 2 gives related work. Section 3 presents problem formulation. Section 4 presents the distributed heuristic. Performance evaluations are done in Section 5 and Section 6 concludes the paper.

Related Work

The sensor coverage problem has been extensively studied in the literature. Depending on the subject covered, most existing works can be classified into area coverage, point coverage, and barrier coverage [2]. In terms of area coverage, many works focus on how to preserve the coverage degree with minimum number of sensors (e.g., 1-degree or k-degree) but they provide no network lifetime guarantee [3-6], [9-11].

The model of point coverage is studied in with the objective to maximize the network lifetime only a given set of targets needs to be covered [1], [15]. Energy-efficient sensing coverage protocol was proposed to achieve full coverage to a certain geographic area [1]. It is also guaranteed to achieve a certain degree of coverage for fault tolerance. And also find the schedules for sensors watching targets that achieve the maximum lifetime. But it has the limitation that each sensor can watch at most one target at a time. When the coverage requirement cannot be satisfied all the time, e.g., in presence of partial coverage, there are routing protocols proposed in to ensure the delivery of the data to the sink in the store-and-forward fashion over the intermittent link [14].In order to configure a network dynamically and to achieve assured degrees of coverage and connectivity a protocol is proposed [4]. That is the Coverage Configuration Protocol (CCP), it provide different degrees of coverage as requested by applications. This flexibility allows the network to self-configure for a wide range of applications.

The node-scheduling scheme can reduce system overall energy consumption, therefore increasing network lifetime, by turning off some redundant nodes [3]. It preserves the system coverage to the maximum extent. Even after the node-scheduling scheme turns off some nodes, certain redundancy is still guaranteed. But for increasing the sensor network lifetime it decreases the bandwidth via local collaboration among nodes.

The centralized algorithms for sensor monitoring schedule to minimize total life time and approximation algorithm for sensor network lifetime problem [12]. Using approximate solutions for Minimum Weight Sensor Cover Problem (MWSCP) it provide guarantee for full coverage. Also this system maximizes network lifetime and Optimizes energy consumption. But it requires complete knowledge of network topology, coordinates of sensor locations and initial energy of sensors.

Kasbekar et. al presents coordinate-free distributed scheme that provides provable approximation guarantees on network lifetime, while providing strict coverage guarantees [13]. This distributed algorithm does not require knowledge of the locations of nodes or directional information. It ensures the k-coverage of the target field during the network lifetime and maximize high lifetime in sensor network. But it dissipates more energy in transmitting data to a remote cluster-head located far.

Balancing object detection quality and network lifetime is a challenging task in sensor networks. A relaxed sensing coverage— partial coverage where the sensing field is partially sensed by active sensors at any time is a more appropriate approach to balancing object detection quality and battery power consumption [8]. For target tracking and the sensing scheduling algorithm for partial coverage scheme allows sensor nodes to periodically wake up and go back to sleep [17-20]. Thus the concept of partial coverage will meet the required average and worst case object detection quality while minimizing network energy consumption. This analytical framework provides accurate guidelines for sensing scheduling protocol design and optimal sensor network deployment. But this system do not treat network lifetime as an objective or constraint.

To minimize energy consumption and extend network lifetime, a common technique is to put some sensors in the sleep mode and put the others in the active mode for the sensing and communication tasks [3], [21]. Optimal Sleep Scheduling was proposed to evaluate the problem of minimizing surveillance delay subject to energy constraints [21]. It improves coverage. But this system supports only a single mission and do not treat network lifetime as the objective or constraint. When a sensor is in the sleep mode it shuts down except that a low-power timer is on to wake up the sensor at a later time, therefore it consumes only a tiny fraction of the energy consumed in the active mode. Moreover, in cluster-based networks, cluster heads are usually selected in a way that minimizes the total energy consumption and they may rotate among the sensors to balance energy consumption.

An optimal polynomial time algorithm uses graph theoretic and computational geometry constructs was proposed for solving for best and worst case coverage. It improves coverage and maximizes network lifetime. But the previously deployed resources may not meet the changing mission requirements all the time [16].

Pyan et al addresses a multiple target coverage problem (MTCP) of WSNs in which different sensors will monitor different numbers of targets and a sensor that monitors more targets would gather more data; hence it will consume more transmission energy [24]. This system proposes an energy efficient sensor scheduling schemes for multiple target coverage (MTC) which maximize the network lifetime by considering both the number of targets covered by the sensor and the redundancy of overlapped targets. Although these schemes are interesting, and heuristic algorithms have been developed and theoretical results are not available.

Problem Formulation

The purpose of the scheduling is to place the on-periods within each cycle, such that the total spatial-temporal coverage can be maximized. We formalize it as a maxiCover problem in Section 2.1, and then, transform it to a miniRedun problem in Section 2.2 whose objective is to minimize the overall coverage redundancy.

3.1 Maximize Coverage

Problem maxiCover: Let G (N, E) be a disk graph with n nodes, the battery life of each sensor be , i = 1 . . . n, and a network lifetime of L, where , we want to calculate an "on" schedule per cycle for each sensor such that the overall spatial-temporal coverage is maximized.

To quantify coverage, an elementary region can be defined as the minimum region formed by the intersection of a number of sensing disks. The spatial-temporal coverage of each region can be calculated as the product of its area size and the length of time during which the region is covered by at least one sensor.

Let we define some notations that will be used throughout the paper.

For given the node set N and the edge set E of the graph, i.e., = {j | sensor is the neighbor of sensor} where is the sensor and be the neighbor set of sensor i.

I is the index set of the redundant elementary regions, i.e., I = {i | region i is a redundant elementary region}

is the index set of sensors whose intersection of sensing disks forms the redundant elementary region, with || denoting its cardinality.

L is the network lifetime and l is the length of the cycle, so there are number of cycles, assuming is an integer. l should not be too small so that the switch overhead between the on/off states is negligible.

is the battery life of and is the length of’s on-period per cycle. Since there are number of cycles, we have

, are the start and end of sensor’s on-period, respectively; we know,

.

is the area size of the ith redundant elementary region.

is the time during which the redundant elementary region is covered by at least one sensor.

Thus we can calculate the total coverage C as the sum of the product of an area size and coverage time, over all the redundant elementary regions. Thus our objective function and constraints are,

(1)

Such that:

, (2)

, (3)

, . (4)

Minimize the Coverage Redundancy

The spatial-temporal coverage redundancy depends on the area size, the overlapping "on" periods, and the number of sensors that monitor the area in each period. With the concept of spatial-temporal coverage redundancy the problem of "maximizing coverage under the constraint of network lifetime" becomes "minimizing the coverage redundancy under the constraint of network lifetime" (called miniRedun problem).Since coverage redundancy has direct impact with overlapped sensor we assign different weight to different period during which same region is monitored by different sensors.

Some more notations defined in this section are;

be the area overlap (i.e., the size of the overlapping area) between and.

be the time overlap (i.e., the length of the overlapping on-period) between and.

, be the time during which the redundant region is covered by exactly j sensors that include all the sensors in S. S can be an empty set ;

With these notations, the problem miniRedun is formulated as follows, with the objective to minimize the total coverage redundancy R:

(5)

Such that:

, (6)

, (7)

, . (8)

Thus the total coverage redundancy is calculated as the weighted sum of the product of area size and time overlap, first, over all the redundant elementary regions. Specifically, is the time during which the redundant elementary region is covered by exactly j sensors that depends on the schedules of j sensors.

From (1) and (5) we have,

(9)

Since,

.

Note that a set of sensors monitor the elementary region, and each sensor is active for period of time per cycle. So each active period can be decomposed into sub periods according to the different coverage degrees of region ai, i.e., Then we have,

(10)

Combining (9) and (10),

(11)

This is a constant value. This implies that maximizing the total coverage C is equivalent to minimizing the total coverage redundancy R.

Distributed Algorithm Design

In the distributed design, we focus on the pair-wise sensors. Here each node minimizes its own local coverage redundancy, defined as the sum of pair-wise redundancy with its neighbours. Although the global optimal is computationally infeasible to achieve, we can design a class of algorithms in which each node is able to achieve the local optimal if certain conditions can be satisfied. The basic idea is to let each node first generate a random schedule independently. Then, each node adjusts its schedule individually to minimize the local coverage redundancy with its neighbours, until everyone converges to its local optimality.

4.1 Maximal Independent Set (MIS)

The MIS algorithm is a distributed algorithm for the determination of well-organized independent set in the topology graph G of a wireless network [7]. The set is said to be maximal independent set (MIS) if no more edges can be added to generate a bigger independent set, where Independent Set is defined as a subset of nodes among which there is no edge between any two nodes.

Fig 1 shows eight sensors and their weight in a wireless network G. Suppose MIS(degree, largest) is executed, the sensor that has the best weight among its neighbours elects itself as belonging to set and all the other neighbors joins it. Here the sensor S2 and S 7 has the best weight forming a set and

S1

(7)

S 2

(8)

S3

(6)

S4

(2)

S5

(2)

S6

(3)

S7

(5)

S8

(1)

Fig 1: A wireless network G with nodes and their weights

S 1

(7)

S 2

(8)

S 3

(6)

S 4

(2)

S 5

(2)

S 6

(3)

S 7

(5)

S 8

(1)

And the sensor S5 has neighbors’ S1, S4 and S8, but its neighbor S1 and S4 has already joined another set with the best weight and it has a best weight than its neighbor S8 then it forms a set Thus at the end of the execution the MIS is generated and it is depicted in fig 2.

Fig 2: A partition of G into sets by MIS algorithm. Each "double circled" node is assigned as head node.

In general, the algorithm can be denoted as MIS (weight, criteria) where the weight can be ID, degree, energy, etc., and the criteria can be either smallest or largest. The criteria are used to interpret the meaning of best weight, i.e., the smallest or the largest. In this paper we make use of both nodes ID and the degree of nodes for best weight and to generate a best MIS which is used to optimize the node schedule independently.

Algorithm 1: Maximal Independent Set (MIS) Algorithm

Input: Graph G, weight of each node and criteria

Output: Maximal weighted independent set

Procedure:

Each node independently determines whether it belongs to the set by comparing its weight with its neighbours.

For each node

If it has no neighbor it elects itself as belongs to the independent set.

If it has the best weight in the neighbourhood, it elects itself as belongs to the set then the entire neighbor joins it.

If its entire neighbor joins another set then it elects itself as belongs to the independent set.

If one or more neighbour joins another set and it has the best weight. Still it has some neighbours not belonging to any set. It elects itself as belongs to the set then all unassigned neighbor join it.

Repeat the step 2 until every node is assigned to a set.

In MIS algorithm, each node must assign a role: a head node or an ordinary node. The head node is a node with best weight among its neighbors which also organizes the set. The ordinary nodes are those nodes that join the head node. The algorithm terminates by generating maximal weighted independent set determining that all nodes belong to any independent set.

4.2 Local Optimization

Suppose sensor has neighbours. The local optimization problem at is given as,

Given the area overlap between and its neighbours (i.e.,), the individual schedule of its neighbours, we want to decide’s own schedule, such that the local sum of the coverage redundancy with its neighbours can be minimized.

Therefore it is easier to calculate local coverage redundancy) than global redundancy (5). Suppose and be the two sensors having sensing range as r and the distance between them are d. The area overlap and time overlap can be given as,

(12)

In order to provide local optimization, Line traversal algorithm is used. This distributed algorithm optimizes each node to adjust its schedule individually to minimize the local coverage redundancy with its neighbors, until everyone converges to its local optimality.

Consider each node has its own reference cycle. The cycles at different nodes are not required to be synchronized. Each node needs only to know the relative position of its neighbour’s on-period. This can be easily achieved via exchange of hello packets with its neighbours. Note that si’s schedule per cycle is solely determined by the start of its on-period and the end of its on-period, where Then, the objective of local optimization at s0 is to decide (or) within its own reference cycle such that coverage redundancy is minimized.

Algorithm 2: Line Traversal Algorithm

Input: Set generated by MIS and schedules of’s neighbours’

Output: Node’s optimal schedule,

Procedure:

For each node first selects its own reference cycle and places each neighbor’s schedule (i.e., on-period) in the cycle.

Enumerate the set of crucial points in terms of the value of

Sort the crucial set χ in increasing order

Calculate and

/*where neighbor’s of, is coverage redundancy at, is area overlap between and its neighbors, is slope between and. Let traversal start from and A, B denote set of neighbors whose on-period spans across 0 and.*/

Set index of crucial point.

Until χ is empty do

Calculate coverage redundancy at using,

The coverage redundancy increases or decreases linearly as traverses from left to right, and the slope k shifts only at some crucial points, which corresponds to the following four cases:

Case I:

If, then the slope increases by i.e,

Case II:

If then the slope increases by i.e,

Case III:

If then the slope decreases by i.e,

Case IV:

If, then the slope decreases by i.e,

and

Increment j (i.e,)

/*that is the traversal end at

Connect the neighboring points piecewise by lines.

Identify minimum local redundancy and select as’s schedule.

In Line traversal algorithm, node first selects its own reference cycle and places each neighbour’s schedule (i.e., on-period) in the cycle. Then,’s on-period traverses from the left of the cycle to the right of the cycle during which the local redundancy] over the whole range can be recorded. In the end, the points corresponding to the minimum are identified and selected as’s schedule.